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Computing and proving with pivots

Frédéric Meunier — 2013

RAIRO - Operations Research - Recherche Opérationnelle

A simple idea used in many combinatorial algorithms is the idea of . Originally, it comes from the method proposed by Gauss in the 19th century for solving systems of linear equations. This method had been extended in 1947 by Dantzig for the famous simplex algorithm used for solving linear programs. From since, a pivoting algorithm is a method exploring subsets of a ground set and going from one subset to a new one ′ by deleting an element inside and adding an element outside : ′ =  ...

Balancing the stations of a self service “bike hire” system

This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the -delivery TSP defined by Chalasani and Motwani in which, unlike their definition, is part of the input: each vertex of a graph has a certain amount of a commodity and wishes to have an amount equal to (we assume...

Balancing the stations of a self service “bike hire” system

This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the -delivery TSP defined by Chalasani and Motwani in which, unlike their definition, is part of the input: each vertex of a graph has a certain amount of a commodity and wishes to have an amount equal to (we assume...

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